Lie inner ideals are nearly Jordan inner ideals

Abstract

In this note we extend the Lie inner ideal structure of simple Artinian rings developed by Benkart to centrally closed prime algebras A A . New Lie inner ideals, which we call nonstandard, occur when making this extension. A necessary and sufficient condition for A A to have a nonstandard inner ideal is the existence in A A of a zero square element which is not von Neumann regular. Our main tool is a theorem due to Martindale and Miers on the iterates of the derivations of prime rings.